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Abstract Studying complex relaxation behaviors is of critical importance for understanding the nature of glasses. Here we report a Kovacs-like memory effect in glasses, manifested by non-monotonic stress relaxation during two-step high-to-low strains stimulations. During the stress relaxation process, if the strain jumps from a higher state to a lower state, the stress does not continue to decrease, but increases first and then decreases. The memory effect becomes stronger when the atomic motions become highly collective with a large activation energy, e.g. the strain in the first stage is larger, the temperature is higher, and the stimulation is longer. The physical origin of the stress memory effect is studied based on the relaxation kinetics and the in-situ synchrotron X-ray experiments. The stress memory effect is probably a universal phenomenon in different types of glasses.